Uncertainty Estimation for the Brillouin Frequency Shift Measurement Using a Scanning Tandem Fabry–Pérot Interferometer

Abstract

The expanded uncertainty of the measured Brillouin scattering shift frequencies is essential in assessing the measurements of parameters of various materials. We describe the general operation principles of a Brillouin light scattering (BLS) spectrometer with a high-power laser and a scanning tandem Fabry–Pérot interferometer (TFPI) for material characterization. Various uncertainty components have been analyzed for the BLS spectrometer following the Guide to the Expression of Uncertainty in Measurement (GUM). The expanded relative uncertainty in the measured Brillouin frequency shift of 15.70 GHz for polymethyl methacrylate (PMMA) was estimated to be 0.26%. The calculated Brillouin frequency shift (based on material properties of PMMA) was determined to be 15.44 GHz with expanded relative uncertainty of 2.13%. It was shown that the measured and calculated Brillouin frequency shifts for PMMA agree within their expanded uncertainties. The TFPI-based BLS spectrometer can be used to measure the longitudinal modulus of materials with an expanded uncertainty of 1.9%, which is smaller than that of the ultrasonic velocity-based method (estimated to be 2.9%).

Robust acoustic impedance monitoring based on forward stimulated Brillouin scattering in an aluminum-coated optical fiber

“…Three experiments are conducted, with the FUT placed in the air, water, and alcohol, respectively. Multiple FSBS waveforms are acquired in each set of experiments, the calculated γ values from Table 1 indicate that similar experimental results were obtained in the same experimental environment, 16 and the average reflection coefficients at interface 2 are calculated to be r eth ¼ 0.895 and r water ¼ 0.833 when the FUT is placed in ethanol and water, respectively.…”

Uncertainty on Brillouin scattering measurements on bulk materials using a power laser

“…A scanning 6-pass TFPI has been described for BLS measurement. Following the GUM, and with reference [30], we have made detailed analysis and estimation of the uncertainties in the Brillouin frequency shift measurement, which is related to the speed of propagation of phononic waves in bulk materials. The expanded relative uncertainty in measured Brillouin frequency shift is estimated to be 0.26% (coverage factor k=2), which corresponds to an expanded uncertainty of 41 MHz for the measured frequency shift of 15.70 GHz in testing PMMA.…”

“…Another contribution to this term is called Abbe error [28,29]. We base all our estimation on results published in reference [30], which is more detailed.…”

An Improved Method to Compute the Mutual Capacitance between Interdigital Transducers in Radio Frequency Surface Acoustic Wave Filters

“…The capacitance computed by the modified method closely aligns with the results from the commercial FEM solver, with slightly greater differences at the edges compared to the center due to fringing effects accounted for in the FEM simulation. The error associated with the current method was assessed [27,28]. For a given ε e f f value, the error increases monotonically as the spacing between fingers increases.…”